Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems

Evangelia Kalligiannaki*, Markos A. Katsoulakis, Petr Plecháč, Dionisios G. Vlachos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.

Original languageEnglish (US)
Pages (from-to)2599-2620
Number of pages22
JournalJournal of Computational Physics
Volume231
Issue number6
DOIs
StatePublished - Mar 20 2012

Keywords

  • Coarse graining
  • Lattice systems
  • Markov chain Monte Carlo
  • Pattern formation
  • Phase transitions

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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